the quarkyonic phase tranistion and the ffp-njl model in large nc
DESCRIPTION
The Quarkyonic Phase Tranistion and the FFP-NJL Model in Large Nc. Unconfined World. Unconfined World. Quarkyonic World. Confined World O(1). Confined World O(1). Conventional Wisdom. Krzysztof Redlich (Wroclaw, GSI) Chihiro Sasaki (Munich) Rob Pisarski and Yoshimasa Hidaka BNL RBRC. - PowerPoint PPT PresentationTRANSCRIPT
The Quarkyonic Phase Tranistion and the FFP-NJL Model in Large Nc
Krzysztof Redlich (Wroclaw, GSI)
Chihiro Sasaki (Munich)
Rob Pisarski and Yoshimasa Hidaka
BNL RBRC
Confined World
O(1)
Unconfined World
Conventional Wisdom
Will argue real world looks more like large N
Unconfined World
Confined World
O(1)
Quarkyonic World
Large N
Conjectured Phase Diagram for Nc = 3
RHIC
LHC
SPS
FAIR
AGS
Confined
No Baryons
N ~0(1)
Not Chiral
Confined
Baryons
N ~ NcNf
Chiral
Debye Screened
Baryons Number
N ~ Nc
Chiral
2
Color Superconductivity
Liquid Gas Transition
Critical Point
Baryon energy density ~ Meson energy density
Quark Gluon Plasma
Quarkyonic Matter
Confined Matter
T
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Brief Review of Large N
Mesons: quark-antiquark, noninteracting, masses ~
Baryons: N quarks, masses ~ , baryon interactions ~
Spectrum of Low Energy Baryons:
Multiplets with I = J; I,J = 1/2 -> I,J = N/2
The confined world has no baryons!
Confinement at Finite Density:
Generates Debye Screening => Deconfinement at Tc
Quark loops are always small by 1/N_c
For finite baryon fermi energy, confinement is never affected by the presence of quarks!
T_c does not depend upon baryon density!
Finite Baryon Density:
No baryons in the confined phase for
For weakly coupled gas of quarks.
If T < T_c, no free gluons, degrees of freedom are ~ Nc
Unconfined World
Confined World
O(1)
Quarkyonic World
Large N
Quarkyonic Matter:
Confined gas of perturbative
quarks!
Confined: Mesons and Glueballs
Quarkyonic: Quarks and Glueballs
Unconfined: Quakrs and Gluons
Some Properties of Quarkyonic Matter
Quarks inside the Fermi Sea: Perturbative Interactions => At High Density can use
perturbative quark Fermi gas for bulk properties
At Fermi Surface: Interactions sensitive to infrared => Confined baryons
Perturbative high density quark matter is chirally symmetric but confined => violates intuitive
arguments that confinement => chiral symmetry
Quarkyonic matter appears when
(Can be modified if quark matter is bound by interactions. Could be “strange quarkyonic
matter”?
Seems not true for N = 3)
Width of the Transition Region:
Baryons are non-relativistic:
Nuclear physics is in a width of order 1/N around the baryon mass!2
c
Large Nc world looks like our world: Nuclear matter is non-relativistic, and there is a narrow transition between
confined and quarkyonic world
Nf/Nc fixed, large Nc
Confinement not an order parameter
Baryon number is
Large density of states:
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With Redlich and Sasaki
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Virtues of the Skyrmion Treatment of Nuclear Matter
Nuclear matter would like to have energy density and pressure of order N
At low density, except for the rest mass contribution to
energy density, ~ 1/N
Baryons are very massive, and in the Skyrme model, the energy density arises from translational zero modes.
Interactions are small because nucleons are far separated.
When energy density is of order N, however, higher order terms in Skyrme model are important, but correct
parametric dependence is obtained
The Non-Perturbative Fermi Surface:
Deep in the Fermi sea, a momentum of order the Fermi momenta must be exchanged in interactions
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Near the Fermi surface,QuickTime™ and a
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Excitations are confined and color singlet
If form a bound state with negative biding energy =>
Chiral condensate
Condensate breaks translational invariance => crystal
Chiral symmetry breaking of order QuickTime™ and a decompressor
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Quarkyonic phase at most weakly breaks chiral symmetry
Might be parity double and chiral symmetric
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Decoupling probably occurs along at low T probably occurs between confined and quarkyonic worlds. Consistent with Cleymans-Redlich-
Stachel-Braun-Munzinger observations!
Unconfined
Quarkyonic
Confined
Maybe it looks a little like this?
Maybe somewhere
around the AGS there is a
tricritical point where these
worlds merge?
Experiment vs. Lattice
μquark →
Lattice “transition” appears above freezeout line? Schmidt ‘07
N.B.: small change in Tc with μ?
T ↑
Lattice Tc , vs μ
Rather small change in Tc vs μ? Depends where μc is at T = 0. Fodor & Katz ‘06
T ↑
μquark →
Conclusions:
There are three phases of QCD at large N:
Confined
Unconfined
Quarkyonic
They have very different bulk properties
There may be a tri-critical point somewhere near AGS energies
The early observations of Cleymans, Redlich,Braun-Munzinger and Stachel
strongly support that this picture reflects N = 3.